Most of hydraulic formulae assume that the boundary shear stress distribution is uniform over the wetted perimeter. However, for meander channel - floodplain geometry, there is a wide variation in the local shear stress distribution from point to point in the wetted perimeter. Therefore, there is a need to evaluate the shear stress carried by the channel and floodplain boundary at various locations of meander path.
Boundary shear stress measurements at the bend apex of a meander path covering a number of points in the wetted perimeter have been obtained from the semi-log relationship of velocity distribution. For each run of the experiment, shear stress distributions are found. For simple meander channels of Type-II and Type-III, the distribution of boundary shear along the channel perimeter at bend apex section AA of the meander path is shown in Figs.4.3.1-Fig.4.3.6 and Fig.4.4.1-Fig.4.4.6 respectively. For comparison, the mean shear stresses obtained by the velocity distribution approach and energy gradient methods for the simple meander channel are given in Table 4.2.
For meandering channels with floodplain of Type-II and Type-III channels, the boundary shear distributions are shown in Figs.4.5.1-Fig.4.5.6 and Figs.4.6.1-Fig.4.6.6 respectively. For the straight compound channels of Type-I these are shown in Figs.4.7.1 to Fig.4.7.5. For these channels also, the mean shear found from the velocity distribution agrees well with the mean value computed from energy gradient approach. These are given in Table 4.3. The following features can be noted from the figures of boundary shear distribution.
Table 4.2 Summary of boundary shear results for the experimental simple meandering channels observed at bend apex-AA
Channel Type
Run No
Flow depth (cm)
Discharge (cm3/s)
Cross Section
Area (cm2)
Wetted perimeter
(cm)
Overall mean shear stress by energy gradient
approach (N/m2)
Overall mean shear stress by velocity distribution approach (N/m2)
Overall shear force
by energy gradient approach (N/m)
Overall shear force
by velocity distribution approach
(N/m)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MM6 5.31 2357 63.72 22.62 0.897 0.857 0.194 0.203 MM8 6.08 2757 72.96 24.16 0.969 0.918 0.222 0.234 MM10 7.11 3338 85.32 26.22 1.041 0.989 0.260 0.273 MM12 8.55 4191 102.60 29.10 1.065 1.072 0.312 0.310 MM13 9.34 4656 112.08 30.68 1.209 1.136 0.362 0.371 Type-II
Mildly Meandering
Channel
MM15 11.01 5680 132.12 34.02 1.264 1.181 0.402 0.430 HM10 5.3 4191 91.69 26.99 1.790 1.766 0.477 0.483
HM11 5.62 4656 99.02 27.89 1.951 1.844 0.515 0.544 HM12 5.93 5122 106.32 28.77 2.037 1.919 0.553 0.586 HM13 6.18 5515 112.35 29.48 2.069 1.981 0.584 0.610 HM14 6.71 6396 125.54 30.98 2.282 2.107 0.653 0.707 Type-III
Highly Meandering
channel
HM15 7.33 7545 141.69 32.73 2.426 2.250 0.737 0.794
Table 4.3 Summary of boundary shear results for over bank flow condition for the experimental channels observed at bend apex-AA
Channel Type
Run No
Relative depth
( ß)
Discharge (cm3/s)
Total Area (cm2)
Total Wetted Perimete
r (cm)
Observed total shear force
in main channel perimeter (N/m)
Observed total shear force
in floodplain
perimeter (N/m)
Observed % of
shear force in floodplain perimeter (%Sfp)
Overall shear stress by energy gradient approach (N/m2)
Overall shear stress by velocity distribution approach
(N/m2)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
S13 0.15 10007 237.3 72.24 0.240 0.174 42.10 0.442 0.414 S15 0.21 13004 282.6 74.30 0.292 0.265 47.64 0.527 0.557 S17 0.30 19861 375.1 78.50 0.339 0.393 53.70 0.699 0.732 S18 0.36 25329 440.9 81.50 0.357 0.529 59.70 0.822 0.886 Type-I
Straight compound
channel
(α = 3.666) S19 0.41 30844 505.2 84.42 0.403 0.632 61.10 0.942 1.035
MM17 0.12 10107 240.9 85.06 0.427 0.360 45.73 0.733 0.787 MM20 0.17 13005 283.6 86.54 0.418 0.468 52.80 0.863 0.886 MM23 0.21 16762 333.2 88.26 0.372 0.554 59.80 1.013 0.926 MM25 0.25 20523 379.4 89.86 0.441 0.771 63.63 1.154 1.212 MM26 0.30 25661 438.2 91.91 0.487 0.999 67.25 1.333 1.486 Type-II
Sinuous compound
channel (α = 4.808)
MM27 0.34 31358 498.8 94.04 0.515 1.215 70.21 1.517 1.73 HM16 0.08 12757 302.8 201.10 0.627 0.751 54.47 1.574 1.378 HM18 0.18 24487 495.8 203.10 0.699 1.756 71.52 2.577 2.455 HM19 0.19 27185 530.5 203.46 0.797 2.144 72.89 2.76 2.941 HM20 0.21 31299 578.8 203.96 0.795 2.372 74.91 3.01 3.167 HM25 0.27 44412 725.4 205.48 0.819 3.081 78.99 3.77 3.9 Type-III
Highly Sinuous & Trapezoidal compound
channel
(α = 16.08) HM27 0.28 48474 760.2 205.84 0.814 3.206 79.76 3.95 4.02
4.5.1 SIMPLE MEANDER CHANNELS
(i) On comparison of the results with straight uniform channel, it can be seen that there is asymmetrical nature of shear distribution especially where there is predominant curvature effect.
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(ii) The over all mean value of boundary shear stress obtained through the velocity distribution approach compares well with that obtained from energy gradient approach.
(iii) Maximum value of wall shear occurs significantly below the free surface and is located at the inner walls.
4.5.2 MEANDER CHANNELS WITH FLOODPLAIN
(i) For meander channel with floodplain there is also good agreement between the measured mean boundary shear from experiments with that of energy gradient approach.
(ii) The local variation of shear is probably due to the assumption of constant value of k (Von Karman turbulent coefficient) in fitting the logarithmic velocity profile.
(iii) The asymmetrical nature of shear stress distribution is very much evident at the sections of bend apex, confirming the findings of Kar (1977), Bhattacharya (1995) and Patra and Kar (2000).
(iv) For low over bank depths, it can be seen that the maximum value of wall shear stress occurs along the inner side wall of main channel. For higher over-bank depths, the maximum value of wall shear stress occurs along the inner side wall of floodplain.
(v) For higher depths of flow over floodplain, the maximum bed shears is located in the floodplain region and for low over-bank depth the maximum bed shear lies near the inner bed of main channel. Though a general pattern of shear distribution is rather unaffected by the over bank flow depth, the width of floodplain and sinuosity are found to affect the nature of distribution to some extent.
(vi) The percentage of shear carried by flood plain region is found to be more for meandering compound channel when compared to that for straight compound channel.
(vii) Low magnitude of boundary shear is found at the outer walls when compared to that at the inner wall.
4.5.3 STRAIGHT COMPOUND CHANNEL
(i) Symmetrical and uniform nature of boundary shear stress distribution is found for straight compound channel of Type-I when compared to the meandering compound channels of Type-II and Type-III.
(ii) The boundary shear at the main channel junctions are generally found to be more than that compared to other points of the wetted perimeter.
(iii) The total shear carried by flood plain is found to be larger than that of the main channel.
(iv) Boundary shear in the main channel and floodplain regions increases proportionately with the over bank flow depth.
(v) Total shear carried by the wetted perimeter of the compound channel compares well with the energy gradient approach.
4.6 DISTRIBUTION OF RADIAL (TRANSVERSE) VELOCITY